An iterative algorithm for the Cramer-von Mises distance estimator

by Jinhyo Kim and Sangyeol Lee .

Abstract: This article concerns the numerical computing of the Cramer-von Mises distance estimator, which is known to have the desirable statistical properties such as the robustness and efficiency. Here, it is shown that the usual optimization algorithms, such as the Newton-Raphson method and the Bisection method, fail to find the estimator. As an alternative, a derivative-free grid-type algorithm, the Dichotomous Search method, is considered. The simulation results show that the Dichotomous Search method tends to find the estimator correctly.

Key Words: Cramer-von Mises distance, Minimum distance estimator, Unimodal, Derivative-free, Dichotomous Search, Convergence rate

Authors:
Jinhyo Kim, jinkim@stats.snu.ac.kr
Sangyeol Lee, sylee@stats.snu.ac.kr

Editor: John P. Hinde , J.P.Hinde@exeter.ac.uk

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